闭嘴，计算：一个极端的数学宇宙

导读

这篇论文以“闭嘴计算”为引子，讨论一种极端的数学宇宙观：物理实在是否本质上就是数学结构，以及这种强数学实在论是否会导向多重宇宙等形而上学结论。评论主要围绕它和经验科学、主观体验及可检验性的关系展开争论。

HN 关注点：把宇宙等同于数学究竟是有洞见的本体论，还是不可检验、近乎柏拉图式的形而上学想象。

关键词　Mathematical UniverseTegmarkinstrumentalismqualia

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这几条评论里：质疑 2　补充 2

补充从图灵完备性和数学定理作为计算捷径出发，认为无需真实硬件或多重宇宙也能让数学结构“存在”。

我喜欢“实在就是数学”这个想法，也独立想到过，但它很快就变得很怪。我还没读这篇文章，但有两个想法：1. 类似图灵完备性，对内部观察者来说实际物理硬件可能无关紧要；所有图灵完备机器能计算同样的东西，机器内部的观察者无法判断自己运行在什么硬件上。类似地，对于我们宇宙中的观察者（人类）也可能如此。所以也许在足够高的抽象层次上，只有一个数学上可能的宇宙。2. 数学定理是计算的捷径。例如我可以在计算机上把两个数相加，也可以用一条定理只告诉我结果的某个性质，从而避免实际计算。所以如果宇宙只是一个计算，人们有时可以靠定理获得所需信息而不必真正计算它。换句话说，你并不需要实际模拟任何东西，模拟中的对象也能“存在”；因此不需要有承载宇宙运行的硬件。补充：我读了文章，我不同意多重宇宙是必要的。如第1点所说，所有可能的数学实在在足够高抽象层次上可能是同一个。

js8查看英文原文

I like the idea that the reality is just mathematics, I thought about it independently, but it gets weird really fast. I yet to have read this essay, but I had two thoughts: 1. Similar to Turing completeness, actual physical reality might not matter for the internal observer. All Turing-complete machines can calculate same things and observer from the inside of the machine cannot determine on what hardware the machine is implemented. Similarly, this can be case for observers within our universe (humans). So maybe there is, at a high enough level of abstraction, only one mathematically possible universe. 2. The mathematical theorems are shortcuts to computation. For example, I can add two numbers on a computer, or I can use a theorem, which will tell me only some property of the result, but avoids having to do the actual calculation. So if universe is just a computation, one could avoid actually computing it in certain cases by having a theorem that would tell them enough information they need. In other words, you don't actually need to simulate anything in order for objects in simulation to "exist". So there is no need for actual hardware on which the universe runs to exist. Addendum: So I read the essay, and I disagree that the multiverse is necessary. As I already stated in point 1, it can be the case that all possible mathematical realities are the same at high enough level of abstraction.

补充解释“闭嘴计算”是量子力学工具主义/科学谦逊：非经验问题超出科学方法范围。

这被称为量子力学的工具主义进路：我们刻意不去思考波函数等的哲学解释，只关注实验结果。其想法是，无论你选多世界、导波还是哥本哈根解释，可观察量都不变，那又有什么关系？（“shut up and calculate”这个说法比本文更早；我认为是 David Mermin 提出的。）这种做法让一些人不快，要么因为它被视为物理学家缺乏想象力、不去看更大的问题，要么因为它接近20世纪中期已名誉扫地的逻辑实证主义。这些抱怨有道理，但我认为也可把它看作物理学家的谦逊，以及承认这超出其专业领域。“科学”根本上是经验性活动；如果你做没有经验性的思考，它可能仍有价值，但不是科学。“闭嘴计算”是简写，意思是：这些问题不是经验性的，我们作为科学家的工具和方法无法处理它们。它承认他们的能力有限。

Analemma_查看英文原文

This is known as the instrumentalist approach to quantum mechanics, where we deliberately avoid thinking about the philosophical interpretations of things like the wavefunction, and only focus on the results of experiments. The thinking being, the observables don't change regardless of whether you pick MWI or pilot wave or the Copenhagen interpretation, so what does it matter? (The actual phrase "shut up and calculate" is older than this paper; I think David Mermin coined it.) This approach rubs some people the wrong way, either because it's seen as a failure of imagination on the part of physicists to look at the bigger questions, or because it drifts close to the discredited logical positivism of the mid-20th century. Those are valid complaints, but I think it can also be seen as humility on the part of physicists, and an understanding that this is outside their field of expertise. "Science" is a fundamentally empirical exercise; if you're doing thinking without empiricism, it might still be valuable thinking, but it isn't science. "Shut up and calculate" is shorthand for, "Because these questions are not empirical, our tools and methods we have as scientists are not capable of addressing them." It's acknowledging that their powers are limited. (I do think it would be nice if more physicists thought about it anyway, because in their abscence the void has been filled with woo by a bunch of New Age cranks, but that's not a moral obligation on their part)

质疑质疑从“理论可用数学描述”跳到“实在就是数学结构”，并指出数学的人类中心性和单一结构假设。

我同意多数物理学家相信存在外部实在。我同意物理理论旨在描述它如何运作。但我不同意因此可推出我们的物理实在具有数学结构。我的反对理由：没有令人信服的理由认为“纯抽象”数学比人类语言更少人类中心主义；即使数学超越人类，也没有令人信服的理由认为存在一个单一的、统摄宇宙的数学结构，尽管随着物理理论发展我们能越来越精确地预测相互作用结果。也许 Tegmark 在“完整强度”版本中回应了这些点，但鉴于他在本文中如此轻描淡写这些隐藏假设，我不太想深入探究。

n4r9查看英文原文

I agree that most physicists believe that an external reality exists. I agree that physical theories aim to describe how it works. But I disagree that it follows that our physical reality has a mathematical structure. My objections are: - There is no compelling reason to think that "purely abstract" mathematics any less anthropocentric than human language; - Even if mathematics transcends humanity, there is no compelling reason to think that there is a single overarching mathematical structure of the universe, despite being able to predict the outcomes of our interactions to greater and greater accuracy as our physical theories develop. It may be that Tegmark addresses these points in his "full strength" version, but given the way he glosses over these hidden assumptions in this paper, I'm not inclined to dig in and find out.

质疑指出数学宇宙观回避了主观体验/感受质这一最直接的经验事实，且“数学产生实在”缺乏实例。

让我困惑的是，人们在做出这些主张时忽视了自己拥有主体性这一事实。这有一定道理，因为科学本身旨在在实践中去除任何主体性污染，所以那些想在生活其他方面（例如个人实在哲学）也彻底“科学”的人继承了这一理想。但这也是矛盾，因为科学方法论要求我们用经验检验结果：你拥有主体性（即感受质存在）以及它是什么样子，是我们能获得的最直接的经验事实，任何关于宇宙构成的讨论都需要调和它。我认为人们要么说感受质/主体性可由数学（或计算过程）产生，而这才重要，从而把这一点推到一边。但我们没有抽象数学产生任何东西的例子；物理过程产生东西，我们用数学影响其行为——仅此而已！而且，即使数学产生了主体性，它最终仍然以其非数学的明显性存在。我还没见过支持数学具有更高本体论地位的论证，不是像柏拉图“理想形式”那样毫无约束的想象和没有根据。

westoncb查看英文原文

It baffles me that people ignore the fact that they have subjectivity when making these claims. It makes a certain amount of sense since science itself aims to remove any taint of subjectivity in its practice, so folks who want to be thoroughly 'scientific' in other aspects of their lives (e.g. their personal philosophies of reality) carry over over this ideal. But it's also a contradiction since science scientific methodology demands we check our results empirically: the fact that you have subjectivity (i.e. that qualia exist) and what it's like, is the most direct empirical fact we have access to and which needs reconciling in any discussion of the universe's constitution. I think people sort of push this point aside either by saying that qualia/subjectivity could be generated by math (or a computational process), and that's what really matters. But we have no examples of abstract math generating anything; physical processes generate things and we use math to influence their behavior—but that's it! And furthermore, even if math generated subjectivity—it's still there in all of its un-mathematical obviousness at the end of the day. I've yet to see an argument in favor of math having higher ontological status than this which wasn't every bit as unrestrainedly imaginative and unfounded as Plato's 'ideal forms'. I would expect a thoroughgoing adherent to scientific methodology to instead say something on the lines of, "this is outside the domain of science to judge one way or the other; the most we can say is the idea that reality is made of math is one untestable hypothesis among many whose probabilities of correctness each approach zero by dint of their many peers."

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